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    Liang, Yongshun 2009. On the fractional calculus of Besicovitch function. Chaos, Solitons & Fractals, Vol. 42, Issue. 5, p. 2741.

    Feng, De-Jun 2005. The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers. Advances in Mathematics, Vol. 195, Issue. 1, p. 24.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 108, Issue 1
  • July 1990, pp. 97-103

The sum of Rademacher functions and Hausdorff dimension

  • Tian-You Hu (a1) and Ka-Sing Lau (a1)
  • DOI:
  • Published online: 24 October 2008

For 0 < α < 1, let for 0 ≤ x < 1, where is the sequence of Rademacher functions. We give a class of fα so that their graphs have Hausdorff dimension 2 − α. The result is closely related to the corresponding unsolved question for the Weierstrass functions.

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[1]W. A. Beyer . Hausdorff dimension of level sets of some Rademacher series. Pacific J. Math. 12 (1962), 3546.

[2]P. Erdös . On the smoothness properties of a family of Bernoulli convolutions. Amer. J. Math. 62 (1940), 180186.

[4]A. M. Garsia . Arithmetic properties of Bernoulli convolutions. Trans. Amer. Math. Soc. 102 (1962), 409–132.

[5]G. H. Hardy and J. E. Littlewood . Some properties of fractional integrals. Math. Z. 27 (1928), 565606.

[6]B. Jessen and A. Wintner . Distribution functions and the Riemann zeta function. Trans. Amer. Math. Soc. 38 (1935), 4888.

[8]R. D. Mauldin and S. C. Williams . On the Hausdorff dimension of some graphs. Trans. Amer. Math. Soc. 298 (1986), 793803.

[10]A. Wintner . On convergent Poisson convolutions. Amer. J. Math. 57 (1935), 827838.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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